A model hierarchy for predicting the flow in stirred tanks with physics-informed neural networks

Advances in Computational Science and Engineering, vol. 2, pp. 91–129

Abstract

This paper explores the potential of Physics-Informed Neural Networks (PINNs) to serve as Reduced Order Models (ROMs) for simulating the flow field within stirred tank reactors (STRs). We solve the two-dimensional stationary Navier-Stokes equations within a geometrically intricate domain and explore methodologies that allow us to integrate additional physical insights into the model. These approaches include imposing the Dirichlet boundary conditions (BCs) strongly and employing domain decomposition (DD), with both overlapping and non-overlapping subdomains. We adapt the Extended Physics-Informed Neural Network (XPINN) approach to solve different sets of equations in distinct subdomains based on the diverse flow characteristics present in each region. Our exploration results in a hierarchy of models spanning various levels of complexity, where the best models exhibit $ \ell_1 $ prediction errors of less than 1% for both pressure and velocity. To illustrate the reproducibility of our approach, we track the errors over repeated independent training runs of the best identified model and show its reliability. Subsequently, by incorporating the stirring rate as a parametric input, we develop a fast-to-evaluate model of the flow capable of interpolating across a wide range of Reynolds numbers. Although we exclusively restrict ourselves to STRs in this work, we conclude that the steps taken to obtain the presented model hierarchy can be transferred to other applications.

Authors 6

1. Veronika Trávníková corresponding
2. Daniel Wolff Aachen Chair for Computational Analysis of Technical Systems (CATS)

   RWTH Aachen University

   Affiliation as printed

   Chair for Computational Analysis of Technical Systems, RWTH Aachen University, Germany

3. Nico Dirkes Aachen Chair for Computational Analysis of Technical Systems (CATS)

   RWTH Aachen University

   Affiliation as printed

   Chair for Computational Analysis of Technical Systems, RWTH Aachen University, Germany

4. Stefanie Elgeti

   TU Wien

   Affiliation as printed

   Institute for Lightweight Design and Structural Biomechanics, TU Wien, Austria

5. Eric von Lieres

   Forschungszentrum Jülich

   Affiliation as printed

   Institute of Bio- and Geosciences 1: Biotechnology, Forschungszentrum Jülich, Germany

6. Marek Behr Aachen Chair for Computational Analysis of Technical Systems (CATS)

   RWTH Aachen University

   Affiliation as printed

   Chair for Computational Analysis of Technical Systems, RWTH Aachen University, Germany